PWM signal generator, PWM signal generating device, and digital amplifier

ABSTRACT

In a full digital amplifier for an audio amplifier or the like, it is possible to suppress the concentration of an electromagnetic noise emission spectrum at a specific frequency. A sampling period variation type digital filter is realized by varying the coefficient of a noise shaping filter for the delta-sigma modulator of the full digital amplifier depending on a sampling period. This allows the variation in the carrier frequency of the pulse width modulation.

TECHNICAL FIELD

The present invention relates to a PWM signal generator and a PWM signalgeneration device which modulate the pulse width of a digital signal,and a digital amplifier that utilizes the generator and the generationdevice.

BACKGROUND ART

Digital amplifiers using switching amplifiers (class-D amplifiers) havebeen used as audio amplifiers that drive speakers or the like, owing to,for example, the high power efficiency of the digital amplifiers. Thedigital amplifiers are classified as a type to which analog signals areinput or a type to which digital signals are input; digital amplifiersof the latter type are called fully digital amplifiers. The fullydigital amplifier can generate output signals without the need foranalog input signals. The fully digital amplifier thus has advantages ofenabling cost reduction of an audio system and improving performance ofthe audio system while maintaining high energy efficiency.

Operation of a common fully digital amplifier will be described below.An example of a configuration of the fully digital amplifier is shown inFIG. 2. A sound source signal r[i] is a pulse code modulated (PCM)signal. If the sound source signal is obtained from, for example, a CD,the sound source signal r[i] has a sampling frequency of 44.1 kHz. Thesound source signal r[i] is input to an over sampler 4, which thenconverts the sound source signal r[i] into a PCM signal u[k] of 705.6kHz, which is 16 times as high as the sampling frequency of the soundsource signal r[i]. The PCM signal u[k] is then converted, by aquantizer 1, into a PCM signal y[k] having the same sampling period butcoarsely quantized. The resolution of the PCM signal y[k] is determinedby the quantizer 1 and is the same as that of a pulse width modulator 2.The PCM signal y[k] is converted into a pulse width modulated (PWM)signal w(t) by the pulse width modulator 2. A noise-shaping filter 3,compensates for quantization noise generated by the quantizer 1 andsignal distortion generated by the pulse width modulator 2 by feedback,so that an audible frequency component of the PWM signal w(t)corresponds to an audible frequency component of the PCM signal u[k].Thus, the audible frequency component of the PWM signal w(t) correspondsto the sound source signal r[i]. The PWM signal w(t) is supplied to aswitching amplifier 5, which then converts the PWM signal w(t) into apower signal. The power signal then passes through a low-pass filter 6composed of L and C, and is supplied to a speaker that is a load.

Patent Document 1 discloses a low-distortion pulse width modulationsignal generator which allows the signal distortion resulting from thepulse width modulation to be fed back to the noise-shaping filter toreduce harmonic distortion, the low-distortion pulse width modulationsignal generator superposing a feed forward signal for compensation ofthe harmonic distortion on an input to the quantizer.

-   Patent Document 1: Japanese Patent Laid-Open No. 2004-236617

DISCLOSURE OF THE INVENTION Problems to be Solved by the Invention

However, with the conventional fully digital amplifier, since theswitching amplifier is driven by the PWM signal generated by digitalcircuits, a fixed carrier frequency in the pulse width modulation maycause radiation of electromagnetic noise with a high peak at a frequencythat is an integral multiple of the carrier frequency.

FIGS. 24 and 25 show an example of a spectrum of the PWM signalgenerated by the conventional fully digital amplifier. The methoddescribed in Patent Document 3 was used to generate the PWM signal. Aninput signal is a pulse code modulated (PCM) signal with a samplingfrequency of 44.1 kHz which is a sinusoidal wave exhibiting a modulationfactor of 82% with a frequency of 2.7563 kHz. A 31-level symmetric pulsewidth modulator was used for the pulse width modulation and exhibited acarrier frequency of 705.6 kHz. As shown in FIG. 24, possiblequantization noise in an audible frequency region is appropriatelysuppressed. However, as shown in FIG. 25, a high peak of the spectrum isgenerated at frequencies that are equal to every integral multiple ofthe carrier frequency. If these peaks leak owing to electromagneticradiation or the like, AM radios, for example, are electromagneticallyinterfered.

To mitigate the adverse effect of electromagnetic noise in an internaloperation signal and harmonic frequencies thereof, a known methoddynamically varies a clock frequency to spread the spectrum of theelectromagnetic noise. However, the PWM carrier frequency of the pulsewidth modulator 2 needs to be dynamically varied in order to apply themethod of spreading the spectrum, to the fully digital amplifier. Toachieve this, the sampling period of the noise-shaping filter 3, whichis a digital filter, needs to be dynamically varied. However, nonoise-shaping filter has been proposed which maintains desiredcharacteristics even with a dynamic variation in sampling period. Thus,disadvantageously, the spectrum spreading technique has been unable tobe used for the fully digital amplifier.

Thus, the present invention solves these problems. An object of thepresent invention is to provide a PWM signal generator and a PWM signalgeneration device which maintain the desired characteristics whiledynamically varying the carrier frequency of the pulse width modulation,to spread the spectrum of the PWM signal, thus enabling possibleelectromagnetic noise to be effectively prevented, as well as to providea digital amplifier utilizing the generator and the generation device.

Means for Solving the Problems

A method of varying coefficients for calculations in a noise-shapingfilter depending on a sampling period is used as means for realizing anoise-shaping filter that maintains desired characteristics even with avariation in sampling period. In this case, it is necessary not only tovary the coefficient but also to take the configuration of thenoise-shaping filter into account. Furthermore, a design method for thenoise-shaping filter varies depending on, for example, a relationshipbetween the sampling period of an input signal and the sampling periodof an output signal.

Thus, the first aspect of the present invention provides a PWM signalgenerator to which a first PCM signal is input and which outputs a PWMsignal, the PWM signal generator being characterized in that a lowfrequency component of the PWM signal depends on a low frequencycomponent of the first PCM signal, the first PCM signal has a firstsampling period, and the PWM signal is generated by digital means basedon a second PCM signal with a second sampling period, in that the secondsampling period is varied for each sampling period so that the sameperiod may consecutively appear, according to an external instruction ora predetermined sequence, the first sampling period is equal to thesecond sampling period, and a resolution of the second PCM signal iscoarser than that of the first PCM signal, in that the first PCM signalis converted into the second PCM signal by a delta-sigma modulator, thedelta-sigma modulator includes a filter and a quantizer, and the firstPCM signal and the second PCM signal are input to the filter, which thenoutputs a third PCM signal, and in that the third PCM signal isconverted into the second PCM signal through the quantizer, a gain ofthe quantizer is dynamically varied in proportion to a value of thesecond sampling period, and a set of coefficients and a set of functionsfor an internal calculation in the filter are determined and dynamicallyvaried according to the second sampling period.

The second aspect of the present invention provides a PWM signalgenerator to which a first PCM signal is input and which outputs a PWMsignal, the PWM signal generator being characterized in that a lowfrequency component of the PWM signal depends on a low frequencycomponent of the first PCM signal, the first PCM signal has a firstsampling period, and the PWM signal is generated by digital means basedon a second PCM signal with a second sampling period, in that the secondsampling period is varied for each sampling period so that the sameperiod may consecutively appear, according to an external instruction ora predetermined sequence, a timing for sampling of the first PCM signalis obtained by adding a timing between samplings of the second PCMsignal to a timing for sampling of the second PCM signal, and aresolution of the second PCM signal is coarser than that of the firstPCM signal, in that the first PCM signal is converted into the secondPCM signal by a delta-sigma modulator, the delta-sigma modulatorincludes a filter and a quantizer, and the first PCM signal and thesecond PCM signal are input to the filter, which then outputs a thirdPCM signal, and in that the third PCM signal is converted into thesecond PCM signal through the quantizer, a gain of the quantizer isdynamically varied in proportion to a value of the second samplingperiod, and a set of coefficients and a set of functions for an internalcalculation in the filter are determined and dynamically variedaccording to the second sampling period.

The third aspect of the present invention provides a PWM signalgenerator to which a first PCM signal is input and which outputs a PWMsignal, the PWM signal generator being characterized in that a lowfrequency component of the PWM signal depends on a low frequencycomponent of the first PCM signal, the first PCM signal has a firstsampling period which is constant, and the PWM signal is generated bydigital means based on a second PCM signal with a second samplingperiod, in that the second sampling period is varied for each samplingperiod so that the same period may consecutively appear, according to anexternal instruction or a predetermined sequence, and the first PCMsignal is converted into the second PCM signal by a delta-sigmamodulator, in that the delta-sigma modulator includes a filter and aquantizer, and the first PCM signal and the second PCM signal are inputto the filter, which then outputs a third PCM signal, and in that thethird PCM signal is converted into the second PCM signal through thequantizer, a gain of the quantizer is dynamically varied in proportionto a value of the second sampling period, and a set of coefficients anda set of functions for an internal calculation in the filter aredetermined and dynamically varied according to the second samplingperiod, or the second sampling period and a relative relationshipbetween a timing for sampling of the first PCM signal and a timing forsampling of the second PCM signal.

The fourth aspect of the present invention provides a PWM signalgeneration device including the PWM signal generator according to thefirst to third inventions and to which a fourth PCM signal is input, thePWM signal generation device outputting the PWM signal, the PWM signalgeneration device being characterized in that a low frequency componentof the PWM signal depends on the fourth PCM signal, and the fourth PCMsignal has a third sampling period which is constant, and in that thePWM signal generation device includes an over sampler to which thefourth PCM signal is input and which outputs the first PCM signal, andthe third sampling period is longer than the first sampling period.

The fifth aspect of the present invention provides a digital amplifiercharacterized by comprising a switching amplifier driven by a PWM signalgenerated by the PWM signal generation device according to the fourthinvention.

ADVANTAGE OF THE INVENTION

According to the present invention, a carrier frequency for pulse widthmodulation is dynamically varied to spread the spectrum of the PWMsignal to effectively prevent electromagnetic noise, while minimizingsignal distortion to allow maintenance of the desired performance of thePWM signal generator and the digital amplifier utilizing the PWM signalgenerator.

BEST MODE FOR CARRYING OUT THE INVENTION First Embodiment

In a case described below, a sampling period of a PCM signal u[k] is thesame as that of a PCM signal y[k], and this sampling period varies. Theconfiguration of a fully digital amplifier in this case is the same asthat shown in FIG. 2. The configuration of the noise-shaping filter isas shown in FIG. 1.

First, to determine target frequency characteristics of thenoise-shaping filter, the noise-shaping filter in continuous-time isdesigned and expressed with a state variable vector as shown in:x*(t)=A*x*(t)+b*(u*(t)−w(t))v*(t)=c*x*(t)  [Equation 1]

In Equation 1, u*(t) is a continuous time signal corresponding to thePCM signal u[k], w(t) is a PWM signal generated by a pulse widthmodulator, v*(t) is a continuous time signal corresponding to acompensation signal v[k] generated by the noise-shaping filter, andx*(t) is a state variable vector. The continuous time filter isdiscretized in time at a sampling period τ_(k) using a 0th-order hold.However, since the sampling period τ_(k) varies dynamically, betweensamplings, an input signal u*(t) is represented by the value of a timeintermediate between the sampling points. This is shown in FIG. 3.However, the compensation signal v[k] samples the value at a samplingtime. That is, Equations 2 and 3 hold true.u[k]=u*((t _(k) +t _(k−1))/2)  (Equation 2)v[k]=v*(t _(k))  (Equation 3)In these Equations, t_(k) is the kth sampling time. Then, a digitalfilter shown in Equations 4 and 5 is obtained.x[k+1]=A(τ_(k))x[k]+b(τ_(k))u[k]−e(y[k])v[k]=cx[k]  [Equation 4]

$\begin{matrix}{{{A\left( \tau_{k} \right)} = {\exp\left( {A^{*}\tau_{k}} \right)}}{{b\left( \tau_{k} \right)} = {\int_{0}^{\tau_{k}}{{\exp\left( {A^{*}t} \right)}\ {\mathbb{d}{tb}^{*}}}}}{c = c^{*}}{{e\left( {y\lbrack k\rbrack} \right)} = {\int_{0}^{\tau_{k}}{{\exp\left( {A^{*}\left( {\tau_{k} - t} \right)} \right)}b^{*}{w\left( {t_{k} + t} \right)}{\mathbb{d}t}}}}} & \left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack\end{matrix}$

In this case, the state variable vector x[k] for the digital filtercorresponds to the sampled value of the state variable x*(t) for thecontinuous time filter. That is, x[k]=x(t_(k)), t_(k+1)−t_(k)=τ_(k).Thus, even when the sampling period τ_(k) varies for each sampling, adiscrete time filter is ensured to be stable and to offer output/inputtransfer characteristic similar to those of the continuous time filter.

Now, it is assumed that an nth-order filter is designed. In this case,A(τ_(k)) in Equation 4 is an n×n matrix. Consequently, the amount ofdigital filter calculations increases consistently with the number ofcoefficients for the digital filter. Thus, when the continuous timefilter in Equation 1 is designed, a matrix A* is block-diagonalized.Then, a matrix A(τ_(k)) in Equation 4 is also block-diagonalized,enabling a reduction in the number of nonzero coefficients for thedigital filter and thus the amount of digital filter calculations.Moreover, in addition to block-diagonilizing the matrix A*, each of theelements of an output vector c from the continuous time filter inEquation 1 is set to be 1 or 0, thus enabling a further reduction in theamount of digital filter calculations. This is because the output vectoris prevented from being varied by the discretization in time in Equation2.

For the above-described discrete time filter, the 0th-order hold isassumed for the input signal to set the value of the signal betweensample points to be constant. Thus, a variation in sampling period maydistort the signal owing to this assumption. A possible method fordealing with the signal distortion is to interpolate the value of theinput signal between the sample points. Several possible methods can beused for the interpolation.

First, the signal waveform of the input signal between the sample pointsis assumed to be approximated using straight lines. This is shown inFIG. 4. Compared to the use of the 0th-order hold, the 1st-orderapproximation is expected to reduce the signal distortion caused by avariation in sampling period. A hold element used to approximateresponses between the sample points with straight lines is called atriangular hold. The triangular hold is used to interpolate thecontinuous time signal u*(t) to discretize the continuous time filterexpressed by Equation 1, in relation to time. Then, the filter is asshown in Equations 6 and 7. In this case, the compensation signal v[k]is represented by the value of the continuous time signal v*(t) at asample time.x[k+1]=A(τ_(k))x[k]+b ₁(τ_(k))u[k]+b ₂(τ_(k))u[k+1]−e(y[k])v[k]=cx[k]  [Equation 6]

$\begin{matrix}{{{A\left( \tau_{k} \right)} = {\exp\left( {A^{*}\tau_{k}} \right)}}{{b_{1}\left( \tau_{k} \right)} = {\int_{0}^{\tau_{k}}{\frac{t}{\tau_{k}}{\exp\left( {A^{*}t} \right)}\ {\mathbb{d}{tb}^{*}}}}}{{b_{2}\left( \tau_{k} \right)} = {\int_{0}^{\tau_{k}}{\left( {1 - \frac{t}{\tau_{k}}} \right){\exp\left( {A^{*}t} \right)}\ {\mathbb{d}{tb}^{*}}}}}{c = c^{*}}{{e\left( {y\lbrack k\rbrack} \right)} = {\int_{0}^{\tau_{k}}{{\exp\left( {A^{*}\left( {\tau_{k} - t} \right)} \right)}b^{*}{w\left( {t_{k} + t} \right)}{\mathbb{d}t}}}}} & \left\lbrack {{Equation}\mspace{14mu} 7} \right\rbrack\end{matrix}$

The digital filter is not strictly proper but includes a feedthroughterm from the input to the output.

Now, the signal waveform of the input signal between the sample pointsis assumed to be approximated with 2nd-order polynomial curves. This isshown in FIG. 5. Compared to the 1st-order approximation, the 2nd-orderapproximation is expected to reduce the signal distortion caused by avariation in sampling period. Here, the value of u*(t) att_(k)≦t≦t_(k)+2 is subjected to 2nd-order approximation using the valuesof u(t_(k)), u(t_(k+1)) and u(t_(k+2)). The value of k is odd. Then, theu*(t) subjected to the 2nd-order approximation is as shown in Equations8 and 9.

$\begin{matrix}{{u^{*}(t)} = {{u\lbrack k\rbrack} + {\left( {{p_{0}{u\lbrack k\rbrack}} + {p_{1}{u\left\lbrack {k + 1} \right\rbrack}} + {p_{2}{u\left\lbrack {k + 2} \right\rbrack}}} \right)t} + {\left( {{q_{0}{u\lbrack k\rbrack}} + {q_{1}{u\left\lbrack {k + 1} \right\rbrack}} + {q_{2}{u\left\lbrack {k + 2} \right\rbrack}}} \right)t^{2}}}} & \left\lbrack {{Equation}\mspace{14mu} 8} \right\rbrack \\{{p_{0} = {- \frac{{2\tau_{k}} + \tau_{k + 1}}{\tau_{k}\left( {\tau_{k} + \tau_{k + 1}} \right)}}},{p_{1} = \frac{\tau_{k} + \tau_{k + 1}}{\tau_{k}\tau_{k + 1}}},{p_{2} = {{{- \frac{\tau_{k}}{\tau_{k + 1}\left( {\tau_{k} + \tau_{k + 1}} \right)}}q_{0}} = \frac{1}{\tau_{k}\left( {\tau_{k} + \tau_{k + 1}} \right)}}},{q_{1} = {- \frac{1}{\tau_{k}\tau_{k + 1}}}},{q_{2} = \frac{1}{\tau_{k + 1}\left( {\tau_{k} + \tau_{k + 1}} \right)}}} & \left\lbrack {{Equation}\mspace{14mu} 9} \right\rbrack\end{matrix}$

The interpolated time function is used to discretize the continuous timefilter expressed by Equation 1, in relation to time. Then, the filter isas shown in Equations 10 to 13. The compensation signal v[k] isrepresented by the value of the continuous time signal v*(t) at thesample time.x[k+1]=A(τ_(k))x[k]+b ₀ ^(o) u[k]+b ₁ ^(o) u[k+1]+b ₂ ^(o)u[k+2]−e(y[k])v[k]=cx[k]  [Equation 10]

$\begin{matrix}{{{A\left( \tau_{k} \right)} = {\exp\left( {A^{*}\tau_{k}} \right)}}{b_{0}^{o} = {\int_{0}^{\tau_{k}}{\left( {1 + {p_{0}t} + {q_{0}t^{2}}} \right){\exp\left( {A^{*}\left( {\tau_{k} - t} \right)} \right)}\ {\mathbb{d}{tb}^{*}}}}}{b_{1}^{o} = {\int_{0}^{\tau_{k}}{\left( {{p_{1}t} + {q_{1}t^{2}}} \right){\exp\left( {A^{*}\left( {\tau_{k} - t} \right)} \right)}\ {\mathbb{d}{tb}^{*}}}}}{b_{2}^{o} = {\int_{0}^{\tau_{k}}{\left( {{p_{2}t} + {q_{2}t^{2}}} \right){\exp\left( {A^{*}\left( {\tau_{k} - t} \right)} \right)}\ {\mathbb{d}{tb}^{*}}}}}{c = c^{*}}{{e\left( {y\lbrack k\rbrack} \right)} = {\int_{0}^{\tau_{k}}{{\exp\left( {A^{*}\left( {\tau_{k} - t} \right)} \right)}b^{*}{w\left( {t_{k} + t} \right)}{\mathbb{d}t}}}}} & \left\lbrack {{Equation}\mspace{14mu} 11} \right\rbrack\end{matrix}$x[k+2]=A(τ_(k+1))x[k+1]+b ₀ ^(e) u[k]+b ₁ ^(e) u[k+1]+b ₂ ^(e)u[k+2]−e(y[k+1])v[k+1]=cx[k+1]  [Equation 12]

$\begin{matrix}{{{A\left( \tau_{k + 1} \right)} = {\exp\left( {A^{*}\tau_{k + 1}} \right)}}{b_{0}^{e} = \mspace{59mu}{\int_{\tau_{k}}^{\tau_{k} + \tau_{k + 1}}{\left( {1 + {p_{0}t} + {q_{0}t^{2}}} \right){\exp\left( {A^{*}\left( {\tau_{k} + \tau_{k + 1} - t} \right)} \right)}\ {\mathbb{d}{tb}^{*}}}}}{b_{1}^{o} = {\int_{\tau_{k}}^{\tau_{k} + \tau_{k + 1}}{\left( {{p_{1}t} + {q_{1}t^{2}}} \right){\exp\left( {A^{*}\left( {\tau_{k} + \tau_{k + 1} - t} \right)} \right)}\ {\mathbb{d}{tb}^{*}}}}}{b_{2}^{o} = {{\int_{\tau_{k}}^{\tau_{k} + \tau_{k + 1}}{\left( {{p_{2}t} + {q_{2}t^{2}}} \right){\exp\left( {A^{*}\left( {\tau_{k} + \tau_{k + 1} - t} \right)} \right)}\ {\mathbb{d}{tb}^{*}}c}} = {{c^{*}{e\left( {y\left\lbrack {k + 1} \right\rbrack} \right)}} = \mspace{50mu}{\int_{\tau_{k}}^{\tau_{k} + \tau_{k + 1}}{{\exp\left( {A^{*}\left( {\tau_{k} + \tau_{k + 1} - t} \right)} \right)}\; b^{*}{\quad{{w\left( {\tau_{k} + t} \right)}{\mathbb{d}t}}}}}}}}} & \left\lbrack {{Equation}\mspace{14mu} 13} \right\rbrack\end{matrix}$

The continuous time signal u*(t) is interpolated and approximated usingthe values of the PCM signal u[k] at three consecutive sampling times.Thus, the filter calculation at an odd number sample time is differentfrom that at an even number sample time. Furthermore, causality does nothold true for the digital filter. Consequently, the digital filter canbe used only if the input signal can be foreseen one sample earlier orif the output signal can be delayed one sample.

Second Embodiment

An alternative method is assumed in which the continuous time signalu*(t) is subjected to 2nd-order interpolation such that the signalvalues between the sample points are interpolated using the values ofthe input signals at the sampling times and the value of the inputsignal at one point between the sampling times for the filtercalculation. This is shown in FIG. 6. Compared to the above-describedmethod, this method reduces the sample intervals for the input signal.This can be expected to reduce the signal distortion caused by avariation in sampling period.

It is assumed that the PCM signal u[k] is the value of the u*(t) at eachsampling time for a loop shaping filter and that the input signalbetween the sample points is newly sampled for every pair of thesampling points and then input. The time between the sample points whenthe signal is sampled is optional. Here, sampling is assumed to beperformed at the time corresponding to the intermediate point betweenthe sample points. The signal corresponding to the intermediate point isassumed to be u_(c)[k]. The value of u*(t) where t_(k)≦t≦t_(k+1) can besubjected to 2nd-order approximation using the values of u[k], u[k+1],and u_(c)[k], as shown in Equation 14.

$\begin{matrix}{{u^{*}(t)} = {{u\lbrack k\rbrack} + {\left( {{{- 3}{u\lbrack k\rbrack}} + {4\;{u_{c}\lbrack k\rbrack}} - {u\left\lbrack {k + 1} \right\rbrack}} \right)\frac{t}{\tau_{k}}} + {\left( {{2\;{u\lbrack k\rbrack}} - {4\;{u_{c}\lbrack k\rbrack}} + {2\;{u\left\lbrack {k + 1} \right\rbrack}}} \right)\frac{t^{2}}{\tau_{k}^{2}}}}} & \left\lbrack {{Equation}\mspace{14mu} 14} \right\rbrack\end{matrix}$

The interpolated time function is used to discretize the continuous timefilter expressed by Equation 1, in relation to time. Then, the resultingfilter is as shown in Equations 15 and 16. The compensation signal v[k]is represented by the value of the continuous time signal v*(t) at thesample time.x[k+1]=A(τ_(k))x[k]+b ₀ ^(c) u[k]+b ₁ ^(c) u _(c) [k]+b ₂ ^(c)u[k+1]−e(y[k])v[k]=cx[k]  [Equation 15]

$\begin{matrix}{{{{A\left( \tau_{k} \right)} = {\exp\left( {A^{*}\tau_{k}} \right)}}{b_{0}^{c} = {\int_{0}^{\tau_{k}}{\left( {1 - {3t} + {2t^{2}}} \right){\exp\left( {A^{*}\left( {\tau_{k} - t} \right)} \right)}\ {\mathbb{d}{tb}^{*}}}}}b_{1}^{c} = {\int_{0}^{\tau_{k}}{\left( {{4t} - {4t^{2}}} \right){\exp\left( {A^{*}\left( {\tau_{k} - t} \right)} \right)}\ {\mathbb{d}{tb}^{*}}}}}{b_{2}^{c} = {\int_{0}^{\tau_{k}}{\left( {{- t} + {2t^{2}}} \right){\exp\left( {A^{*}\left( {\tau_{k} - t} \right)} \right)}\ {\mathbb{d}{tb}^{*}}}}}{c = {{c^{*}{e\left( {y\lbrack k\rbrack} \right)}} = {\int_{0}^{\tau_{k}}{{\exp\left( {A^{*}\left( {\tau_{k} - t} \right)} \right)}\; b^{*}{\quad{{w\left( {t_{k} + t} \right)}{\mathbb{d}t}}}}}}}} & \left\lbrack {{Equation}\mspace{14mu} 16} \right\rbrack\end{matrix}$

The digital filter is not strictly proper and includes a feedthroughterm from the input to the output.

Third Embodiment

Now, it is assumed that the sampling period of the PCM signal u[h] isconstant, whereas the sampling period of the PCM signal y[k] varies. Thenoise-shaping filter is operated in synchronism with the sampling of thePCM signal y[k]. The configuration of the fully digital amplifier inthis case is shown in FIG. 7. The constant sampling period of the PCMsignal u[h] enables the signal distortion caused by a dynamic variationin sampling period of the noise-shaping filter to be minimized. Also inthis case, the target dynamic characteristics of the noise-shapingfilter are assumed to be provided by the continuous time filterexpressed by Equation 1.

Sampling of the PCM signal u[h] is assumed to take place at most oncebetween the sample points of the PCM signal y[k]. The 0th-order hold isapplied to the PCM signal u[h]. This is shown in FIG. 8. The outputsignal v[k] is assumed to be represented by the value of the signal atthe sample time. Such a digital filter is as shown in Equations 18, 19,21, and 22. Here, the time when the input u[h] is sampled is defined ast^(u) _(h). The time when the output y[k] is sampled is defined ast_(k).

When (Equation 17) t^(u) _(h)≦t_(k)<t_(k+1)<t^(u) _(h+1), that is, whenno input signal is sampled between output sample points, the resultingfilter is as shown in Equations 18 and 19.x[k+1]=A(τ_(k))x[k]+b(τ_(k))u[h]−e(y[k])v[k]=cx[k]  [Equation 18]

$\begin{matrix}{{{A\left( \tau_{k} \right)} = {\exp\left( {A^{*}\tau_{k}} \right)}}{{b\left( \tau_{k} \right)} = {\int_{0}^{\tau_{k}}{{\exp\left( {A^{*}t} \right)}{\mathbb{d}{tb}^{*}}}}}{c = c^{*}}{{e\left( {y\lbrack k\rbrack} \right)} = {\int_{0}^{\tau_{k}}{{\exp\left( {A^{*}\left( {\tau_{k} - t} \right)} \right)}\; b^{*}{\quad{{w\left( {t_{k} + t} \right)}{\mathbb{d}t}}}}}}} & \left\lbrack {{Equation}\mspace{14mu} 19} \right\rbrack\end{matrix}$

Furthermore, whent ^(u) _(h) ≦t _(k) <t ^(u) _(h+1) ≦t _(k+1) <t ^(u) _(h+2)  (Equation20)that is, when the input signal is sampled once between the output samplepoints, the resulting filter is as shown in Equations 21 and 22.x[k+1]=A(τ_(k))x[k]+b ₃(τ_(k) ,t _(k+1) −t _(h+1) ^(u))u[h]+b(t _(k+1)−t _(h+1) ^(u))u[h+1]−e(y[k])v[k]=cx[k]  [Equation 21]

$\begin{matrix}{{{A\left( \tau_{k} \right)} = {\exp\left( {A^{*}\tau_{k}} \right)}}{{b\left( {t_{k + 1} - t_{h + 1}^{u}} \right)} = {\int_{0}^{t_{k + 1} - t_{h + 1}}{{\exp\left( {A^{*}t} \right)}\ {\mathbb{d}{tb}^{*}}}}}{{b_{3}\left( {\tau_{k},{t_{k + 1} - t_{h + 1}^{u}}} \right)} = {\int_{t_{k + 1} - t_{h + 1}}^{\tau_{k}}{{\exp\left( {A^{*}t} \right)}\ {\mathbb{d}{tb}^{*}}}}}{c = c^{*}}{{e\left( {y\lbrack k\rbrack} \right)} = {\int_{0}^{\tau_{k}}{{\exp\left( {A^{*}\left( {\tau_{k} - t} \right)} \right)}\; b^{*}{\quad{{w\left( {t_{k} + t} \right)}{\mathbb{d}t}}}}}}} & \left\lbrack {{Equation}\mspace{14mu} 22} \right\rbrack\end{matrix}$

It is assumed that for the addition of the u[h] to the v[k], the valueof the u[h] corresponding to the time immediately before t_(k) is addedto the v[k]. The above-described method has applied the 0th-order holdto the PCM signal u[h]. However, the noise-shaping filter can besimilarly designed even if the triangular hold or any otherinterpolation method is used.

It is assumed that calculations for the noise-shaping filter areperformed according to the sampling period of the PCM signal u[h]. ThePCM signal y[k] has a dynamically varying sampling period and thus doesnot always synchronize with the calculation period of the noise-shapingfilter. The 0th-order hold is used for the PCM signal u[h] to discretizethe continuous time filter expressed by Equation 1, in relation to time.In this discretization, using the PWM signal w(t) as the feedback signalincreases the size of a table required for the calculations for thenoise-shaping filter. Thus, the PWM signal w(t) is approximated by thePCM signal y[k].

Here, the desired noise-shaping filter is as follows. When τ^(u)=t^(u)_(h+1)−t^(u) _(h), the desired noise-shaping filter is as shown inEquations 24, 26, and 27.

Ift _(k−1) ≦t ^(u) _(h) ≦t _(k) <t ^(u) _(h+1) <t _(k+1)  (Equation 23)the resulting filter is as shown in Equation 24.x[h+1]=A(τ^(u))x[k]+b(τ^(u))u[h]−b ₃(τ^(u) ,t _(h+1) ^(u) −t_(k))y[k−1]−b(t _(h+1) ^(u) −t _(k))y[k]v[k]=c ₁(t _(k) −t _(h) ^(u))x[h]+d ₃(t _(k) −t _(h)^(u))(u[h]−y[k−1])  [Equation 24]Ift _(k−1) ≦t ^(u) _(h) ≦t _(k) <t _(k+1) <t ^(u) _(h+1)  (Equation 25)the resulting filter is as shown in Equations 26 and 27.

$\begin{matrix}\begin{matrix}{{x\left\lbrack {h + 1} \right\rbrack} = {{{A\left( \tau^{u} \right)}{x\lbrack k\rbrack}} + {{b\left( \tau^{u} \right)}{u\lbrack h\rbrack}} - {b_{3}\left( {\tau^{u},{t_{h + 1}^{u} - t_{k}}} \right)}}} \\{{y\left\lbrack {k - 1} \right\rbrack} - {{b_{3}\left( {{t_{h + 1}^{u} - t_{k}},{t_{h + 1}^{u} - t_{k + 1}}} \right)}{y\lbrack k\rbrack}} -} \\{{b\left( {t_{h + 1}^{u} - t_{k + 1}} \right)}{y\lbrack k\rbrack}} \\{{v\lbrack k\rbrack} = {{{c_{1}\left( {t_{k} - t_{h}^{u}} \right)}{x\lbrack h\rbrack}} + {{d_{3}\left( {t_{k} - t_{h}^{u}} \right)}\left( {{u\lbrack h\rbrack} - {y\left\lbrack {k - 1} \right\rbrack}} \right)}}} \\{{v\left\lbrack {k + 1} \right\rbrack} = {{{c_{1}\left( {t_{k + 1} - t_{h}^{u}} \right)}{x\lbrack h\rbrack}} + {{d_{3}\left( {t_{k + 1} - t_{k}} \right)}\left( {{u\lbrack h\rbrack} - {y\lbrack k\rbrack}} \right)} +}} \\{{d_{4}\left( {{t_{k + 1} - t_{h}^{u}},{t_{k + 1} - t_{k}}} \right)}\left( {{u\lbrack h\rbrack} - {y\left\lbrack {k - 1} \right\rbrack}} \right)}\end{matrix} & \left\lbrack {{Equation}\mspace{14mu} 26} \right\rbrack \\{\;{{{A\left( \tau^{u} \right)} = {\exp\left( {A^{*}\tau^{u}} \right)}}{{b\left( \tau^{u} \right)} = {\int_{0}^{\tau^{u}}{{\exp\left( {A^{*}t} \right)}\ {\mathbb{d}{tb}^{*}}}}}{{b_{3}\left( {\tau^{u},{t_{h + 1}^{u} - t_{k}}} \right)} = {\int_{t_{h + 1}^{u} - t_{k}}^{\tau^{u}}{{\exp\left( {A^{*}t} \right)}\ {\mathbb{d}{tb}^{*}}}}}{{c_{1}\left( {t_{k} - t_{h}^{u}} \right)} = {c^{*}\exp\left\{ {A^{*} \cdot \left( {t_{k} - t_{h}^{u}} \right)} \right\}}}{{d_{3}\left( {t_{k + 1} - t_{h}^{u}} \right)} = {c^{*}{\int_{0}^{t_{k + 1} - t_{h}^{u}}{{\exp\left( {A^{*}t} \right)}\ {\mathbb{d}{tb}^{*}}}}}}{{d_{4}\left( {{t_{k + 1} - t_{h}^{u}},{t_{k + 1} - t_{k}}} \right)} = {c^{*}{\int_{t_{k + 1} - t_{k}}^{t_{k + 1} - t_{h}^{u}}{{\exp\left( {A^{*}t} \right)}\ {\mathbb{d}{tb}^{*}}}}}}}} & \left\lbrack {{Equation}\mspace{14mu} 27} \right\rbrack\end{matrix}$

It is assumed that in the addition of the u[h] to the v[k], the value ofthe u[h] corresponding to the time immediately before the t_(k) is addedto the v[k]. The above-described method has been assumed to use the0th-order hold for the input. However, the digital filter can besimilarly designed if the use of the hold is avoided or if thetriangular hold is used.

First Example

The present example corresponds to a fully digital audio amplifier thatuses a PWM signal with a dynamically varying carrier period. Theconfiguration of the audio amplifier is as shown in FIGS. 1 and 2. Asound source signal r[i] is a PCM signal with a sampling frequency of44.1 kHz and is input to an over sampler 4. The over sampler 4 convertsthe sound source signal r[i] into the PCM signal u[k] with the samplinginterval τ_(k). The value of the sampling interval τ_(k) is not constantand is 1/16 (about 1.472 μs) or 15/64 (about 1.329 μs) of that of thesound source signal r[i]. The percentage at which the sampling intervalτ_(k) of the PCM signal u[k] exhibits the 1/16 value is almost the sameas that at which the sampling interval τ_(k) of the PCM signal u[k]exhibits the 15/64 value. Which of the values the sampling intervalτ_(k) of the PCM signal u[k] exhibits is determined by a pseudo-randomnumber. The noise-shaping filter 3 uses the 0th-order interpolation toperform the filter calculations shown in Equations 4 and 5. Thefrequency shaping of quantization noise in the PCM signal y[k], which isthe output signal from the quantizer 1, is thus performed to suppressaudible frequency components of the noise. The number of quantizationsteps in the quantizer 1 is 31 when the sampling interval τ_(k) is 1/16of that of the sound source signal r[i] or 29 when the sampling intervalτ_(k) is 15/64 of that of the sound source signal r[i].

The quantizer 1 associates the signal range (full scale) of the inputsignal with the signal range (full scale) of the output signal. Thesignal range of the input signal is constant, whereas the signal rangeof the output signal varies depending on the sampling interval τ_(k).Thus, a conversion gain of the quantizer 1 needs to be in proportion tothe sampling interval τ_(k). This is expressed by y[k]=round(g*s[k]*τ_(k)). Here, g is an appropriate constant, and s[k] is theinput signal to the quantizer 1. Furthermore, round( ) is a functionhaving an argument that performs a conversion into an integer closest tothe argument.

The pulse width modulator 2 generates the PWM signal according to thePCM signal y[k]. In this case, the period of the carrier signal is equalto the sampling interval τ_(k) and varies dynamically. The generated PWMsignal drives the switching amplifier 5. The switching amplifier 5 thusdrives the speaker, which is a load, through the low-pass filter 6.

Several spectra of the PWM signal w(t) in the fully digital audioamplifier are shown in the figures. FIG. 9 shows an example of aspectrum of the PWM signal w(t) in the vicinity of the audible frequencyregion; the sound source signal is a sinusoidal wave with an amplitudeof a modulation factor of 80% and a frequency of 2.7563 kHz. Although aninsignificant second harmonic is observed, the spectrum shows thatquantization noise in the audible frequency region is suppressed.However, compared to the case in which the sampling period of the u[k]is constant, the present example slightly raises a noise floor in theaudible frequency region because of the adverse effect of aninterpolation error in the signal u[k] in the noise-shaping filter. FIG.10 shows a broad spectrum of the PWM signal w(t). The figure indicatesthat the spectrum is spread by the dynamic variation in the carrierfrequency of the PWM signal. Although the total amount of spectrum doesnot change significantly, concentration of the spectrum at a particularfrequency can be avoided. This allows electromagnetic noise to beprevented.

FIG. 11 shows a spectrum of the PWM signal w(t) in the vicinity of theaudible frequency region; the sound source signal is a sinusoidal wavewith an amplitude of a modulation factor of 80% and a frequency of16.5378 kHz. The spectrum shows that the increased frequency of thesound source signal increases the floor noise in the audible frequencyregion. This is due to the adverse effect of the interpolation error inthe signal u[k] in the noise-shaping filter.

An advantage of the present example is that the use of the concept ofthe 0th-order interpolation for the calculations for the noise-shapingfilter enables a reduction in the amount of calculations.

Second Example

The present example corresponds to a fully digital audio amplifier thatuses a PWM signal with a dynamically varying carrier period. Theconfiguration of the audio amplifier is as shown in FIG. 2. The soundsource signal r[i] is a PCM signal with a sampling frequency of 44.1 kHzand is input to the over sampler 4. The over sampler 4 converts thesound source signal r[i] into the PCM signal u[k] with the samplinginterval τ_(k). The value of the sampling interval τ_(k) is not constantand is 1/16 (about 1.472 μs) or 15/64 (about 1.329 μs) of that of thesound source signal r[i]. The percentage at which the sampling intervalτ_(k) of the PCM signal u[k] exhibits the 1/16 value is almost the sameas that at which the sampling interval τ_(k) of the PCM signal u[k]exhibits the 15/64 value. Which of the values the sampling intervalτ_(k) of the PCM signal u[k] exhibits is determined by a pseudo-randomnumber. The noise-shaping filter 3 uses the 1st-order interpolation toperform the filter calculations shown in Equations 6 and 7. The spectrumof the quantization noise in the PCM signal y[k], which is the outputsignal from the quantizer 1, is thus shaped to suppress its audiblefrequency components. The number of quantization steps in the quantizer1 is 31 when the sampling interval τ_(k) is 1/16 of that of the soundsource signal r[i] or 29 when the sampling interval τ_(k) is 15/64 ofthat of the sound source signal r[i].

The quantizer 1 associates the signal range (full scale) of the inputsignal with the signal range (full scale) of the output signal. Thesignal range of the input signal is constant, whereas the signal rangeof the output signal varies depending on the sampling interval τ_(k).Thus, the conversion gain of the quantizer 1 needs to be in proportionto the sampling interval τ_(k). This is expressed by y[k]=round(g*s[k]*τ_(k)). Here, g is the appropriate constant, and s[k] is theinput signal to the quantizer 1. Furthermore, round( ) is the functionthat performs conversion into the integer closest to the argument.

The pulse width modulator 2 generates the PWM signal according to thePCM signal y[k]. In this case, the period of the carrier signal is equalto the sampling interval τ_(k) and varies dynamically. The generated PWMsignal drives the switching amplifier 5. The switching amplifier 5 thusdrives the speaker, which is a load, through the low-pass filter 6.

Several spectra of the PWM signal w(t) in the fully digital audioamplifier are shown in the figures. FIG. 12 shows an example of aspectrum of the PWM signal w(t) in the vicinity of the audible frequencyregion; the sound source signal is a sinusoidal wave with an amplitudeof a modulation factor of 80% and a frequency of 2.7563 kHz. Although aninsignificant second harmonic is observed, the spectrum shows thatquantization noise in the audible frequency region is suppressed.Compared to the case in which the sampling period of the signal u[k] isconstant, the present example slightly raises the noise floor in theaudible frequency region because of the adverse effect of theinterpolation error in the signal u[k] in the noise-shaping filter.However, the raise is more suppressed by virtue of the 1st-orderinterpolation compared to FIG. 9, where the 0th-order interpolation isused. FIG. 13 shows a broad spectrum of the PWM signal w(t). The figureindicates that the spectrum is spread by the dynamic variation in thecarrier frequency of the PWM signal. Although the total amount ofspectrum does not change significantly, the concentration of thespectrum at a particular frequency can be avoided. This allows theelectromagnetic noise to be prevented.

FIG. 14 shows a spectrum of the PWM signal w(t) in the vicinity of theaudible frequency region; the sound source signal is a sinusoidal wavewith an amplitude of a modulation factor of 80% and a frequency of16.5378 kHz. The spectrum shows that the increased frequency of thesound source signal increases the floor noise in the audible frequencyregion. This is due to the adverse effect of the interpolation error inthe signal u[k] in the noise-shaping filter. The floor noise has almostthe same magnitude as that observed with the 0th-order interpolation.

An advantage of the present example is that compared to the use of the0th-order interpolation, the use of the concept of the 1st-orderinterpolation for the calculations for the noise-shaping filter reducesthe floor noise caused by the interpolation error without significantlyincreasing the amount of calculations when the sound source signal has alow frequency.

Third Example

The present example corresponds to a fully digital audio amplifier thatuses a PWM signal with a dynamically varying carrier period. Theconfiguration of the audio amplifier is as shown in FIG. 2. The soundsource signal r[i] is a PCM signal with a sampling frequency of 44.1 kHzand is input to the over sampler 4. The over sampler 4 converts thesound source signal r[i] into the PCM signal u[k] with the samplinginterval τ_(k). The value of the sampling interval τ_(k) is not constantand is 1/16 (about 1.472 μs) or 15/64 (about 1.329 μs) of that of thesound source signal r[i]. The percentage at which the sampling intervalτ_(k) of the PCM signal u[k] exhibits the 1/16 value is almost the sameas that at which the sampling interval τ_(k) of the PCM signal u[k]exhibits the 15/64 value. Which of the values the sampling intervalτ_(k) of the PCM signal u[k] exhibits is determined by a pseudo-randomnumber. The noise-shaping filter 3 performs the filter calculationsbased on the concept of the 2nd-order interpolation and shown inEquations 10 to 13. The spectrum of the quantization noise in the PCMsignal y[k], which is the output signal from the quantizer 1, is thusshaped to suppress the audible frequency components. The number ofquantization steps in the quantizer 1 is 31 when the sampling intervalτ_(k) is 1/16 of that of the sound source signal r[i] or 29 when thesampling interval τ_(k) is 15/64 of that of the sound source signalr[i].

The quantizer 1 associates the signal range (full scale) of the inputsignal with the signal range (full scale) of the output signal. Thesignal range of the input signal is constant, whereas the signal rangeof the output signal varies depending on the sampling interval τ_(k).Thus, the conversion gain of the quantizer 1 needs to be in proportionto the sampling interval τ_(k). This is expressed by y[k]=round(g*s[k]*τ_(k)). Here, g is an appropriate constant, and s[k] is theinput signal to the quantizer 1. Furthermore, round( ) is the functionthat performs conversion into the integer closest to the argument.

The pulse width modulator 2 generates the PWM signal according to thePCM signal y[k]. In this case, the period of the carrier signal is equalto the sampling interval τ_(k) and varies dynamically. The generated PWMsignal drives the switching amplifier 5. The switching amplifier 5 thusdrives the speaker, which is a load, through the low-pass filter 6.

Several spectra of the PWM signal w(t) in the fully digital audioamplifier are shown in the figures. FIG. 15 shows an example of aspectrum of the PWM signal w(t) in the vicinity of the audible frequencyregion; the sound source signal is a sinusoidal wave with an amplitudeof a modulation factor of 80% and a frequency of 2.7563 kHz. Thespectrum shows that the second harmonic is successfully suppressed andthat the quantization noise in the audible frequency region is alsosuppressed. The adverse effect of the interpolation error in the signalu[k] in the noise-shaping filter is insignificant enough to be hidden bythe quantization error. FIG. 16 shows a broad spectrum of the PWM signalw(t). The figure indicates that the spectrum is spread by the dynamicvariation in the carrier frequency of the PWM signal. Although the totalamount of spectrum does not change significantly, the concentration ofthe spectrum at a particular frequency can be avoided. This allows theelectromagnetic noise interferences to be prevented.

FIG. 17 shows a spectrum of the PWM signal w(t) in the vicinity of theaudible frequency region; the sound source signal is a sinusoidal wavewith an amplitude of a modulation factor of 80% and a frequency of16.5378 kHz. The spectrum shows that the increased frequency of thesound source signal increases the floor noise in the audible frequencyregion. This is due to the adverse effect of the interpolation error inthe signal u[k] in the noise-shaping filter. The floor noise has almostthe same magnitude as that observed with the 0th-order interpolation.

An advantage of the present example is that compared to the use of the1st-order interpolation, the use of the concept of the 2nd-orderinterpolation for the calculations for the noise-shaping filter reducesthe floor noise caused by the interpolation error without significantlyincreasing the amount of calculations when the sound source signal has alow frequency.

Fourth Example

The present example corresponds to a fully digital audio amplifier thatuses a PWM signal with a dynamically varying carrier period. Theconfiguration of the audio amplifier is similar to that shown in FIG. 2except that the over sampler 4 outputs not only the PCM signal u[k] butalso the u_(c)[k] and that the u_(c)[k] is additionally input to thenoise-shaping filter 3. The sound source signal r[i] is a PCM signalwith a sampling frequency of 44.1 kHz and is input to the over sampler4. The over sampler 4 converts the sound source signal r[i] into the PCMsignal u[k] with the sampling interval τ_(k). The value of the samplinginterval τ_(k) is not constant and is 1/16 (about 1.472 μs) or 15/64(about 1.329 μs) of that of the sound source signal r[i]. The percentageat which the sampling interval τ_(k) of the PCM signal u[k] exhibits the1/16 value is almost the same as that at which the sampling intervalτ_(k) of the PCM signal u[k] exhibits the 15/64 value. Which of thevalues the sampling interval τ_(k) of the PCM signal u[k] exhibits isdetermined by a pseudo-random number. The noise-shaping filter 3performs the filter calculations based on the concept of the 2nd-orderinterpolation and shown in Equations 15 and 16. The spectrum of thequantization noise in the PCM signal y[k], which is the output signalfrom the quantizer 1, is thus shaped to suppress the audible frequencycomponents. The number of quantization steps in the quantizer 1 is 31when the sampling interval τ_(k) is 1/16 of that of the sound sourcesignal r[i] or 29 when the sampling interval τ_(k) is 15/64 of that ofthe sound source signal r[i].

The quantizer 1 associates the signal range (full scale) of the inputsignal with the signal range (full scale) of the output signal. Thesignal range of the input signal is constant, whereas the signal rangeof the output signal varies depending on the sampling interval τ_(k).Thus, the conversion gain of the quantizer 1 needs to be in proportionto the sampling interval τ_(k). This is expressed by y[k]=round(g*s[k]*τ_(k)). Here, g is the appropriate constant, and s[k] is theinput signal to the quantizer 1. Furthermore, round( ) is the functionthat performs conversion into the integer closest to the argument.

The pulse width modulator 2 generates the PWM signal according to thePCM signal y[k]. In this case, the period of the carrier signal is equalto the sampling interval τ_(k) and varies dynamically. The generated PWMsignal drives the switching amplifier 5. The switching amplifier 5 thusdrives the speaker, which is a load, through the low-pass filter 6.

Several spectra of the PWM signal w(t) in the fully digital audioamplifier are shown in the figures. FIG. 18 shows an example of aspectrum of the PWM signal w(t) in the vicinity of the audible frequencyregion; the sound source signal is a sinusoidal wave with an amplitudeof a modulation factor of 80% and a frequency of 2.7563 kHz. Thespectrum shows that the second harmonic is successfully suppressed andthat the quantization noise in the audible frequency region is alsosuppressed. The adverse effect of the interpolation error in the signalu[k] in the noise-shaping filter is insignificant enough to be hidden bythe quantization error. FIG. 19 shows a broad spectrum of the PWM signalw(t). The figure indicates that the spectrum is spread by the dynamicvariation in the carrier frequency of the PWM signal. Although the totalamount of spectrum does not change significantly, the concentration ofthe spectrum at a particular frequency can be avoided. This allows theelectromagnetic noise interferences to be prevented.

FIG. 20 shows a spectrum of the PWM signal w(t) in the vicinity of theaudible frequency region; the sound source signal is a sinusoidal wavewith an amplitude of a modulation factor of 80% and a frequency of16.5378 kHz. The spectrum shows that the floor noise in the audiblefrequency region is prevented from being increased in spite of theincreased frequency of the sound source signal. This is due to the useof the value u_(c)[k] between the sample points for the interpolation ofthe signal u[k] in the noise-shaping filter, which reduces theinterpolation error.

An advantage of the present example is that the floor noise caused bythe interpolation error can be reduced by using the value between thesample points for the calculations in the noise-shaping filter and alsousing the concept of the 2nd-order interpolation.

Fifth Example

The present example corresponds to a fully digital audio amplifier thatuses a PWM signal with a dynamically varying carrier period. Theconfiguration of the audio amplifier is as shown in FIG. 7. The soundsource signal r[i] is a PCM signal with a sampling frequency of 44.1 kHzand is input to the over sampler 4. The over sampler 4 converts thesound source signal r[i] into the PCM signal u[h] with a samplingfrequency of 705.6 kHz, which is 16 times as high as the samplingfrequency of the sound source signal r[i]. The noise-shaping filter 3and the quantizer 1 output the PCM signal y[k] with the samplinginterval τ_(k). The value of the sampling interval τ_(k) is not constantand is 1/16 (about 1.472 μs) or 13/16 (about 1.152 μs) of that of thePCM signal u[h]. The rate at which the sampling interval τ_(k) of thePCM signal u[h] exhibits the 1/16 value is almost the same as that atwhich the sampling interval τ_(k) of the PCM signal u[h] exhibits the13/16 value. Which of the values the sampling interval τ_(k) of the PCMsignal u[h] exhibits is determined by a pseudo-random number. Thenoise-shaping filter 3 performs the filter calculations based on theconcept of the 0th-order interpolation and shown in Equations 17 to 22.The frequency of the quantization noise in the PCM signal y[k], which isthe output signal from the quantizer 1, is thus shaped to suppress theaudible frequency components. The number of quantization steps in thequantizer 1 is 31 when the sampling interval τ_(k) is 1/16 of that ofthe sound source signal r[i] or 25 when the sampling interval τ_(k) is13/64 of that of the sound source signal r[i].

The quantizer 1 associates the signal range (full scale) of the inputsignal with the signal range (full scale) of the output signal. Thesignal range of the input signal is constant, whereas the signal rangeof the output signal varies depending on the sampling interval τ_(k).Thus, the conversion gain of the quantizer 1 needs to be in proportionto the sampling interval τ_(k). This is expressed by y[k]=round(g*s[k]*τ_(k)). Here, g is the appropriate constant, and s[k] is theinput signal to the quantizer 1. Furthermore, round( ) is the functionthat performs conversion into the integer closest to the argument.

The pulse width modulator 2 generates the PWM signal according to thePCM signal y[k]. In this case, the period of the carrier signal is equalto the sampling interval τ_(k) and varies dynamically. The generated PWMsignal drives the switching amplifier 5. The switching amplifier 5 thusdrives the speaker, which is a load, through the low-pass filter 6.

Several spectra of the PWM signal w(t) in the fully digital audioamplifier are shown in the figures. FIG. 21 shows an example of aspectrum of the PWM signal w(t) in the vicinity of the audible frequencyregion; the sound source signal is a sinusoidal wave with an amplitudeof a modulation factor of 80% and a frequency of 2.7563 kHz. Thespectrum shows that the second harmonic is successfully suppressed andthat the quantization noise in the audible frequency region is alsosuppressed. The constant sampling period of the PCM signal u[h] preventsthe floor noise caused by the adverse effect of the interpolation error.FIG. 22 shows a broad spectrum of the PWM signal w(t). The figureindicates that the spectrum is spread by the dynamic variation in thecarrier frequency of the PWM signal. Although the total amount ofspectrum does not change significantly, the concentration of thespectrum at a particular frequency can be avoided. This allows theelectromagnetic noise interferences to be prevented. In this case, thecarrier frequency is allowed to vary significantly to more widely spreadthe spectrum.

FIG. 23 shows a spectrum of the PWM signal w(t) in the vicinity of theaudible frequency region; the sound source signal is a sinusoidal wavewith an amplitude of a modulation factor of 80% and a frequency of16.5378 kHz. The spectrum shows that the floor noise increase in theaudible frequency region is prevented in spite of the increasedfrequency of the sound source signal.

An advantage of the present example is that the constant sampling periodof the PCM signal u[h] prevents the floor noise caused by theinterpolation error in PCM signal u[h].

Another advantage of the present example is that the sampling intervalof the PCM signal y[k], that is, the range of variation in the carrierperiod of the PWM signal w(t), can be increased to allow the spectrum ofthe PWM signal to be sufficiently spread.

In the present example, the noise-shaping filter 3 has performed thefilter calculations shown in Equations 17 to 22, for each samplingperiod of the PCM signal y[k]. However, the filter calculations shown inEquations 23 to 27 may be performed for each sampling period of theu[h].

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing a configuration of a noise-shapingfilter;

FIG. 2 is a block diagram showing a configuration of a fully digitalamplifier;

FIG. 3 is a diagram showing a relationship between variable samplingsignals observed in the case that a 0th-order hold is used according toa first embodiment of the present invention;

FIG. 4 is a diagram showing a relationship between variable samplingsignals observed in the case that 1st-order approximation is usedaccording to the first embodiment of the present invention;

FIG. 5 is a diagram showing the relationship between the variablesampling signals observed in the case that 2nd-order approximation isused according to the first embodiment of the present invention;

FIG. 6 is a diagram showing the relationship between the variablesampling signals observed in the case that 2nd-order interpolation isused according to a second embodiment of the present invention;

FIG. 7 is a block diagram showing a configuration of a fully digitalamplifier according to a third embodiment of the present invention;

FIG. 8 is a diagram showing the relationship between the variablesampling signals observed in the case that the 0th-order hold is usedaccording to the third embodiment of the present invention;

FIG. 9 is a diagram of a spectrum of a pulse width modulated signal inthe vicinity of an audible frequency region according to a first exampleof the present invention;

FIG. 10 is a diagram of a broad spectrum of the pulse width modulatedsignal in the first example of the present invention;

FIG. 11 is a diagram of a spectrum of a pulse width modulated signal inthe vicinity of the audible frequency region with respect to a soundsource signal with a high frequency in the first example of the presentinvention;

FIG. 12 is a diagram of a spectrum of a pulse width modulated signal inthe vicinity of the audible frequency region according to a secondexample of the present invention;

FIG. 13 is a diagram of a broad spectrum of the pulse width modulatedsignal in the second example of the present invention;

FIG. 14 is a diagram of a spectrum of a pulse width modulated signal inthe vicinity of the audible frequency region with respect to a soundsource signal with a high frequency in the second example of the presentinvention;

FIG. 15 is a diagram of a spectrum of a pulse width modulated signal inthe vicinity of the audible frequency region according to a thirdexample of the present invention;

FIG. 16 is a diagram of a broad spectrum of the pulse width modulatedsignal in the third example of the present invention;

FIG. 17 is a diagram of a spectrum of a pulse width modulated signal inthe vicinity of the audible frequency region with respect to a soundsource signal with a high frequency in the third example of the presentinvention;

FIG. 18 is a diagram of a spectrum of a pulse width modulated signal inthe vicinity of the audible frequency region according to a fourthexample of the present invention;

FIG. 19 is a diagram of a broad spectrum of the pulse width modulatedsignal in the fourth example of the present invention;

FIG. 20 is a diagram of a spectrum of a pulse width modulated signal inthe vicinity of the audible frequency region with respect to a soundsource signal with a high frequency in the fourth example of the presentinvention;

FIG. 21 is a diagram of a spectrum of a pulse width modulated signal inthe vicinity of the audible frequency region according to a fifthexample of the present invention;

FIG. 22 is a diagram of a broad spectrum of the pulse width modulatedsignal in the fifth example of the present invention;

FIG. 23 is a diagram of a spectrum of a pulse width modulated signal inthe vicinity of the audible frequency region with respect to a soundsource signal with a high frequency in the fifth example of the presentinvention;

FIG. 24 is a diagram of a spectrum, in the vicinity of the audiblefrequency region, of a pulse width modulated signal generated accordingto the conventional art; and

FIG. 25 is a diagram of a broad spectrum of a pulse width modulatedsignal generated according to the conventional art.

DESCRIPTION OF SYMBOLS

-   1 Quantizer-   2 Pulse width modulator-   3 Noise-shaping filter-   31 Delay element-   32 Square matrix-   33 Output vector-   34 Input vector-   35 Nonlinear function vector-   36 Nonlinear element-   4 Over sampler-   5 Switching amplifier-   6 Low-pass filter

What is claimed is:
 1. A PWM signal generator comprising: a first PCMsignal that is input into the PWM signal generator, the first PCM signalhaving a first sampling period; a second PCM signal having a secondsampling period, wherein the second sampling period is varied for eachsampling period so that the same period may consecutively appear,according to an external instruction or a predetermined sequence, and aresolution of the second PCM signal is coarser than that of the firstPCM signal; a delta-sigma modulator that converts the first PCM signalinto the second PCM signal, the delta-sigma modulator including a filterand a quantizer, wherein the first PCM signal and the second PCM signalare input into the filter, which then outputs a third PCM signal, andthe quantizer converts the third PCM signal into the second PCM signaland a gain of the quantizer is dynamically varied in proportion to avalue of the second sampling period, and a set of coefficients and a setof functions for an internal calculation in the filter are determinedand dynamically varied according to the second sampling period; and aPWM signal that is output from the PWM signal generator, wherein the PWMsignal is generated by digital means based on the second PCM signal. 2.The PWM signal generator of claim 1, further comprising: a fourth PCMsignal that is input into the PWM signal generator; and an over samplerto which the fourth PCM signal is input and which outputs the first PCMsignal, wherein a low frequency component of the PWM signal depends onthe fourth PCM signal, and the fourth PCM signal has a third samplingperiod that is constant, the third sampling period being longer than thefirst sampling period.
 3. A digital amplifier comprising: a switchingamplifier; and the PWM signal generator of claim 2, wherein the PWMsignal generated by the PWM signal generator drives the switchingamplifier.
 4. A PWM signal generator comprising: a first PCM signal thatis input into the PWM signal generator, the first PCM signal having afirst sampling period; a second PCM signal having a second samplingperiod, wherein the second sampling period is varied for each samplingperiod so that the same period may consecutively appear, according to anexternal instruction or a predetermined sequence, the first samplingperiod being equal to the second sampling period, and a resolution ofthe second PCM signal is coarser than that of the first PCM signal; adelta-sigma modulator that converts the first PCM signal into the secondPCM signal, the delta-sigma modulator including a filter and aquantizer, wherein the first PCM signal and the second PCM signal areinput into the filter, which then outputs a third PCM signal, and thequantizer converts the third PCM signal into the second PCM signal and again of the quantizer is dynamically varied in proportion to a value ofthe second sampling period, and a set of coefficients and a set offunctions for an internal calculation in the filter are determined anddynamically varied according to the second sampling period; and a PWMsignal that is output from the PWM signal generator, wherein the PWMsignal is generated by digital means based on the second PCM signal. 5.The PWM signal generator of claim 4, further comprising: a fourth PCMsignal that is input into the PWM signal generator; and an over samplerthat is part of the PWM signal generator, the fourth PCM signal beinginput to the over sampler, the over sampler outputting the first PCMsignal, wherein a low frequency component of the PWM signal depends onthe fourth PCM signal, and the fourth PCM signal has a third samplingperiod which is constant, the third sampling period being longer thanthe first sampling period.
 6. A digital amplifier comprising: aswitching amplifier; and the PWM signal generator of claim 5, whereinthe PWM signal generated by the PWM signal generator drives theswitching amplifier.
 7. A PWM signal generator comprising: a first PCMsignal that is input into the PWM signal generator, the first PCM signalhaving a first sampling period; a second PCM signal having a secondsampling period, wherein the second sampling period is varied for eachsampling period so that the same period may consecutively appear,according to an external instruction or a predetermined sequence, asequence of instants for sampling of the first PCM signal is obtained byadding a sequence of instants between samplings of the second PCM signalto a sequence of instants for sampling of the second PCM signal, and aresolution of the second PCM signal is coarser than that of the firstPCM signal; a delta-sigma modulator that converts the first PCM signalinto the second PCM signal, the delta-sigma modulator including a filterand a quantizer, wherein the first PCM signal and the second PCM signalare input into the filter, which then outputs a third PCM signal, andthe quantizer converts the third PCM signal into the second PCM signaland a gain of the quantizer is dynamically varied in proportion to avalue of the second sampling period, and a set of coefficients and a setof functions for an internal calculation in the filter are determinedand dynamically varied according to the second sampling period; and aPWM signal that is output from the PWM signal generator, wherein the PWMsignal is generated by digital means based on the second PCM signal. 8.The PWM signal generator of claim 7, further comprising: a fourth PCMsignal that is input into the PWM signal generator; and an over samplerto which the fourth PCM signal is input and which outputs the first PCMsignal, wherein a low frequency component of the PWM signal depends onthe fourth PCM signal, and the fourth PCM signal has a third samplingperiod that is constant, the third sampling period being longer than thefirst sampling period.
 9. A digital amplifier comprising: a switchingamplifier; and the PWM signal generator of claim 8, wherein the PWMsignal generated by the PWM signal generator drives the switchingamplifier.
 10. A PWM signal generator comprising: a first PCM signalthat is input into the PWM signal generator, the first PCM signal havinga first sampling period that is constant; a second PCM signal having asecond sampling period, wherein the second sampling period is varied foreach sampling period so that the same period may consecutively appear,according to an external instruction or a predetermined sequence, and aresolution of the second PCM signal is coarser than that of the firstPCM signal; a delta-sigma modulator that converts the first PCM signalinto the second PCM signal, the delta-sigma modulator including a filterand a quantizer, wherein the first PCM signal and the second PCM signalare input into the filter, which then outputs a third PCM signal, andthe quantizer converts the third PCM signal into the second PCM signaland a gain of the quantizer is dynamically varied in proportion to avalue of the second sampling period, and a set of coefficients and a setof functions for an internal calculation in the filter are determinedand dynamically varied according to the second sampling period, or thesecond sampling period and a relative relationship between a timing forsampling of the first PCM signal and a timing for sampling of the secondPCM signal; and a PWM signal that is output from the PWM signalgenerator, wherein the PWM signal is generated by digital means based onthe second PCM signal.
 11. The PWM signal generator of claim 10, furthercomprising: a fourth PCM signal that is input into the PWM signalgenerator; and an over sampler to which the fourth PCM signal is inputand which outputs the first PCM signal, wherein a low frequencycomponent of the PWM signal depends on the fourth PCM signal, and thefourth PCM signal has a third sampling period that is constant, thethird sampling period being longer than the first sampling period.
 12. Adigital amplifier comprising: a switching amplifier; and the PWM signalgenerator of claim 11, wherein the PWM signal generated by the PWMsignal generator drives the switching amplifier.